You have at your disposal the best program in the current educational market to delve into the development of arithmetic and numeracy skllls, through dozens of hours of theoretical and practical content”

Mathematics and its component branches represent a challenge of understanding for the student, and of teaching for the professional. Its understanding must be approached from the first school levels to avoid that famous difficulty that characterizes it. A solid initial base explained through numerical games and advanced methodologies will lay the foundations for a fluid learning process.

Therefore, the teacher specialized in this area needs constant updating and continuous improvement of their skills when transmitting knowledge to their own students. In this context, TECH has created this Postgraduate certificate, whose objective is to enable students to update their skills in the teaching of numeracy in Pre-school Education. This way, through a 100% online methodology that allows you to manage your study schedules according to your needs and obligations, the student will obtain an efficient learning and will acquire the necessary skills to advance towards an informal and intuitive arithmetic in Pre-school Education.

To do so, they will have 150 hours of the best theoretical and practical content, which they will be able to access at any time and place, only needing a device with an internet connection. In addition, you will have at your disposal a large amount of complementary material in the form of detailed videos, dynamic summaries of each unit, complementary readings, frequently asked questions and much more, which will help you to boost your career and position yourself as an expert in a high-demand sector.

Delve into the stages in the teaching-learning of magnitudes and boost your professional career thanks to this Postgraduate certificate”

This Postgraduate certificate in Arithmetic, Algebra, Geometry, and Measurement in Pre-School Education.Number Games contains the most complete and up-to-date educational program on the market. The most important features include:

• The development of practical cases presented by experts in Arithmetic, Algebra, Geometry and Measurement. in Pre-School
• The graphic, schematic, and practical contents with which they are created, provide practical information on the disciplines that are essential for professional practice
• Practical exercises where the self-assessment process can be carried out to improve learning
• Its special emphasis on innovative methodologies 
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with an Internet connection

Enroll now and delve into the development of pre-linguistic numerical skills in pre-school education”

The program’s teaching staff includes professionals from the sector who contribute their work experience to this training program, as well as renowned specialists from leading societies and prestigious universities. 

The multimedia content, developed with the latest educational technology, will provide the professional with situated and contextual learning, i.e., a simulated environment that will provide immersive education programmed to learn in real situations. 

The design of this program focuses on Problem-Based Learning, by means of which the professional must try to solve the different professional practice situations that are presented throughout the academic course. For this purpose, the students will be assisted by an innovative interactive video system created by renowned and experienced experts.  

An unique opportunity to establish comparison of counting concepts in Piaget’s, Gelman’s and Gallistel’s Theory"

Take advantage of all the tools offered by this Postgraduate certificate and access them 24 hours a day, establishing your own pace of study"

TECH is a pioneer in the field of education for the use of the revolutionary Relearning methodology for the development of all its programs. Thanks to the continuous reiteration of the most important concepts throughout the syllabus, the student acquires new knowledge in a natural and progressive way. Therefore, leaving behind the tedious task of memorization, the graduate who completes this program will delve into the numerical spatial arrangement to delve in a more detailed way in the procedures used by the child in counting.

Learn strategies to enhance the concept and use of number with a program that allows you to distribute the teaching load according to your needs”

Module 1. Arithmetic, Algebra, Geometry and Measurement Games with Numbers

1.1. Initiation to Number

1.1.1. Number Concept
1.1.2. Construction of the Number Structure
1.1.3. Numerical Development: Counting

1.1.3.1. Phases in Learning the Numerical Sequence

1.1.3.1.1. Rope or String Level
1.1.3.1.2. Unbreakable Chain Level
1.1.3.1.3. Breakable Chain Level
1.1.3.1.4. Numerable Chain Level
1.1.3.1.5. Bidirectional Chain Level

1.1.4. Counting Principles

1.1.4.1. One-to-one Correspondence Principle
1.1.4.2. Stable Order Principle
1.1.4.3. Cardinality Principle
1.1.4.4. Abstraction Principle
1.1.4.5. Irrelevance of Order Principle

1.1.5. Procedures used by the Child in Counting

1.1.5.1. Term to Term Correspondence
1.1.5.2. Subset to Subset Correspondence
1.1.5.3. Purely Visual Estimation
1.1.5.4. Subitizing
1.1.5.5. Count the Elements of a Collection
1.1.5.6. Recount
1.1.5.7. Discount
1.1.5.8. Overcount
1.1.5.9. Calculation Procedures

1.1.6. Fundamental Cardinal and Ordinal Situations
1.1.7. The Importance of Zero
1.1.8. Strategies to Enhance the Concept and Use of Number

1.2. Number Acquisition Process

1.2.1. Introduction
1.2.2. Number Concept

1.2.2.1. Perception of General Quantities
1.2.2.2. Distinguishing and Comparing Quantities of Objects
1.2.2.3. Uniqueness Principle
1.2.2.4. Generalization
1.2.2.5. Summative Action
1.2.2.6. Capture of Named Quantities

1.2.2.6.1. Oral Numeric Series
1.2.2.6.2. Counting Objects
1.2.2.6.3. Cardinal Representation
1.2.2.6.4. Compare Magnitudes

1.2.2.7. Identification of the Name with its Representation
1.2.2.8. Invariance of Named Quantities

1.2.3. From Experimental Psychology

1.2.3.1. Distance Effect
1.2.3.2. Size Effect
1.2.3.3. Numerical Spatial Arrangement

1.2.4. From Developmental Psychology

1.2.4.1. Behavioral, Cognitive and Constructivist Theory

1.2.4.1.1. Exercise Law
1.2.4.1.2. Law of Effect

1.2.5. Theories on the Process of Number Acquisition
1.2.6. Piaget

1.2.6.1. Stages
1.2.6.2. Requirements for the Understanding of the Notion of Number

1.2.7. Dienes

1.2.7.1. Principles

1.2.7.1.1. Dynamic Principle
1.2.7.1.2. Constructive Principle
1.2.7.1.3. Economic Variability Principle
1.2.7.1.4. Constructive Variability Principle

1.2.7.2. Stages

1.2.7.2.1. Free Play
1.2.7.2.2. Game with Rules
1.2.7.2.3. Isomorphic Games
1.2.7.2.4. Representation
1.2.7.2.5. Description
1.2.7.2.6. Deduction

1.2.8. Mialaret

1.2.8.1. Stages

1.2.8.1.1. Action Itself
1.2.8.1.2. Action Accompanied by Language
1.2.8.1.3. Conduct of the Narrative
1.2.8.1.4. Application of the Story to real Situations
1.2.8.1.5. Graphical Expression of the Actions already Reported and Represented
1.2.8.1.6. Symbolic Translation of the Studied Problem

1.2.9. Information Processing

1.2.9.1. Numerical Apprehension Model
1.2.9.2. Pre-linguistic Numerical Skills

1.2.10. Counting Principles (Gelman and Gallistel)

1.2.10.1. Biunivocal Correspondence Principle
1.2.10.2. Stable Order Principle
1.2.10.3. Cardinality Principle
1.2.10.4. Abstraction Principle
1.2.10.5. Inconsequence of Order Principle

1.2.11. Comparison of Counting Principles between Piaget's, Gelman's and Gallistel's Theory

1.3.  Informal Arithmetic I

1.3.1. Introduction
1.3.2. Towards an Informal and Intuitive Arithmetic in Pre-school Education

1.3.2.1. Recognize Quantities
1.3.2.2. Relate Quantities
1.3.2.3. Operate Quantities

1.3.3. Objectives
1.3.4. Early Arithmetic Skills

1.3.4.1. Preservation of Inequality

1.3.5. Arithmetic Skills and Chants

1.3.5.1. Preliminary Considerations

1.3.5.1.1. Socio-Cognitive Conflict
1.3.5.1.2. Role of the Language
1.3.5.1.3. Creation of Contexts

1.3.5.2. Procedures and Mastery of the Chants

1.4. Informal Arithmetic II

1.4.1. Memorization of Numerical Facts

1.4.1.1. Activities to Work on Memorization
1.4.1.2. Domino
1.4.1.3. Hopscotch

1.4.2. Didactic Situations for the Introduction of Addition

1.4.2.1. Dialed Number Game
1.4.2.2. Race to 10
1.4.2.3. Christmas Greeting

1.5. Basic Arithmetic Operations

1.5.1. Introduction
1.5.2. Additive Structure

1.5.2.1. Phases of Mialaret

1.5.2.1.1. Approach Through Manipulation
1.5.2.1.2. Action Accompanied by Language
1.5.2.1.3. Mental Work Supported by Verbalization
1.5.2.1.4. Purely Mental Work

1.5.2.2. Strategies to Add
1.5.2.3. Initiation to Subtraction
1.5.2.4. Addition and Subtraction

1.5.2.4.1. Direct and Object Modeling
1.5.2.4.2. Counting Sequences
1.5.2.4.3. Recalled Numeric Data
1.5.2.4.4. Strategies to Add
1.5.2.4.5. Subtraction Strategies

1.5.3. Multiplication and Division
1.5.4. Arithmetic Problem Solving

1.5.4.1. Addition and Subtraction
1.5.4.2. Multiplications and Divisions

1.6. Space and Geometry in Pre-school Education

1.6.1. Introduction
1.6.2. Objectives Proposed by the NCTM
1.6.3. Psychopedagogical Considerations
1.6.4. Recommendations for Teaching Geometry
1.6.5. Piaget and his Contribution to Geometry
1.6.6. Van Hiele Model

1.6.6.1. Levels

1.6.6.1.1. Visualization or Recognition
1.6.6.1.2. Analysis
1.6.6.1.3. Sorting and Classification
1.6.6.1.4. Rigor

1.6.6.2. Learning Phases

1.6.6.2.1. Phase 1: Consultancy
1.6.6.2.2. Phase 2: Directed Guidance Psychologist's Assessment Phase 3: Explication
1.6.6.2.3. Phase 4: Guidance
1.6.6.2.54. Phase 5: Integration

1.6.7. Geometry Types

1.6.7.1. Topological
1.6.7.2. Projective
1.6.7.3. Metrics

1.6.8. Visualization and Reasoning

1.6.8.1. Spatial Orientation
1.6.8.2. Spatial Structuring
1.6.8.3. Gálvez y Brousseau

1.6.8.3.1. Microspace
1.6.8.3.2. Mesospace
1.6.8.3.3. Macrospace

1.7. Magnitudes and their Measurement

1.7.1. Introduction
1.7.2. Construction of the Notion of Magnitude in the Child

1.7.2.1. Piagetian Phases in the Construction of Magnitudes

1.7.2.1.1. Consideration and Perception of a Magnitude
1.7.2.1.2. Conservation of Magnitude
1.7.2.1.3. Ordering with Respect to Magnitude
1.7.2.1.4. Correspondence of Numbers to Quantities of Magnitude

1.7.2.2. Stages in the Construction of the Measure

1.7.2.2.1. Direct Perceptual Comparison
1.7.2.2.2. Displacement of Objects
1.7.2.2.3. Operability of the Transitive Property

1.7.2.3. Stages in the Teaching-Learning of Magnitudes

1.7.2.3.1. Sensory Stimulation
1.7.2.3.2. Direct Comparison
1.7.2.3.3. Indirect Comparison
1.7.2.3.4. Choice of Unit
1.7.2.3.5. Irregular Measurement System
1.7.2.3.6. Regular Measurement System

1.7.3. Measuring Magnitudes
1.7.4. Length Measurement
1.7.5. Length Measurement
1.7.6. Measurement of Capacity and Volume
1.7.7. Measurement of Time
1.7.8. Phases of the Different Magnitudes

1.7.8.1. Preparation Phase
1.7.8.2. Measurement Practice Phase
1.7.8.3. Consolidation Phase of Techniques and Concepts

1.8. Play in Pre-school Education

1.8.1. Introduction
1.8.2. Objectives
1.8.3. Playing Features
1.8.4. Evolution of the Game

1.8.4.1. Types of Games

1.8.4.1.1. Functional Game
1.8.4.1.2. Imitation or Symbolic Play
1.8.4.1.3. Game with Rules
1.8.4.1.4. Construction Game

1.8.5. Chance and Strategy
1.8.6. Competition in the Games
1.8.7. Didactic Considerations on the Game

1.9. Didactic Resources of the Game

1.9.1. Games and Logical Thinking

1.9.1.1. Three in a Row
1.9.1.2. Quarto
1.9.1.3. Portrait Games

1.9.2. Quantitative Games

1.9.2.1. Number to Compare

1.9.2.1.1. Let’s Go Home!!

1.9.2.2. Number to Calculate

1.9.2.2.1. Couples
1.9.2.2.2. It’s Over!!
1.9.2.2.3. Cat and Mouse

1.9.3. Games and the Structure of Space

1.9.3.1. Puzzles

1.9.3.1.1. Two-Color Paintings
1.9.3.1.2. The Hex

1.10. Games in Different Spaces

1.10.1. Introduction
1.10.2. Games in the Classroom

1.10.2.1. The Butterfly Game
1.10.2.2. The Partitioning Game
1.10.2.3. Image Trains
1.10.2.4. The Newspaper
1.10.2.5. Flat Figures
1.10.2.6. The Containers

1.10.3. Games in Psychomotor Skills

1.10.3.1. Working with Sizes
1.10.3.2. Classify
1.10.3.3. We Play with the Hoops

1.10.4. Outdoor Games
1.10.5. Mathematical Games with ICT

1.10.5.1. Playing with the Turtle's Mind
1.10.5.2. Geometric Figures
1.10.5.3. For 3-Year-Old Students
1.10.5.4. Variety of Activities
1.10.5.5. Didactic Unit

Get into mathematical games through the use of ICT, thanks to the exclusive multimedia content provided by TECH”